本文關(guān)鍵詞： 高中數(shù)學(xué) 算法初步 算法教學(xué)　出處：《內(nèi)蒙古師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：二十世紀數(shù)學(xué)科學(xué)與教育發(fā)生了巨大變革,有兩個重要標志：一是數(shù)學(xué)應(yīng)用領(lǐng)域的變革；二是數(shù)學(xué)與計算機應(yīng)用技術(shù)的同步發(fā)展。計算機之父馮.諾伊曼和圖靈都是著名的數(shù)學(xué)家。一個方面,不論計算機硬件發(fā)展還是計算機軟件升級都離不開算法的設(shè)計,從另一個方面思考,計算機技術(shù)的高速發(fā)展也對數(shù)學(xué)的發(fā)展起到了巨大的推進作用,展了數(shù)學(xué)研究的領(lǐng)域,極大地豐富了數(shù)學(xué)研究的方式方法,加強了數(shù)學(xué)與其它學(xué)科領(lǐng)域的聯(lián)系,拓寬了數(shù)學(xué)的應(yīng)用領(lǐng)域,程序設(shè)計即算法設(shè)計已滲透到很多數(shù)學(xué)分支�！八惴ā笔桥囵B(yǎng)邏輯推理能力的非常好的載體。算法思想是初等數(shù)學(xué)學(xué)習(xí)內(nèi)容的一條主線,是依據(jù)算法邏輯進行內(nèi)容設(shè)計。所謂算法是指按照一些步驟,一步一步解決某一個問題的程序化或機械化思維過程；而所謂邏輯是指個體以客觀真實為依據(jù),按照一定的遞推關(guān)系對問題結(jié)論做出判斷的思維過程。這種一步一步地解決問題之清晰的程序化思想是每一位個體發(fā)展的現(xiàn)實需要。算法并非是一個很陌生的知識,雖然,有些人不太熟悉這個概念,但是,算法思想經(jīng)常出現(xiàn)在很多的數(shù)學(xué)內(nèi)容中。例如,求解方程、方程組、不等式,幾何作圖或證明,求解線性規(guī)劃問題,等等,都可以說是算法問題。算法的特點是可操作、可檢驗,有一些教師在嘗試把“算法”內(nèi)容與計算機程序設(shè)計有機的結(jié)合起來,這對培養(yǎng)學(xué)生學(xué)習(xí)數(shù)學(xué)興趣也有很好的促進作用。對于數(shù)學(xué)教師來說,難度不大,經(jīng)過培訓(xùn),不會有困難,有些地區(qū)采取了一些有效的措施(例如,分成小組,分工備課,集體研討,教案共享),很好地解決了這個問題。“算法”求解或證明問題的方式是通過框圖形式進行展示的,一個問題的算法框圖可以把這個問題的解決過程非常清晰的、非常直觀的、非常簡潔的、非常準確的表示出來�；谔岣咚惴ń虒W(xué)實際效果和不斷提高利用算法思想與方法解決實際問題的能力之觀念,我們從以下幾方面做了一些研究：首先,通過文獻分析和課堂觀察法,了解國內(nèi)外算法教學(xué)研究現(xiàn)狀和高中算法教學(xué)現(xiàn)實狀況與存在問題,明確研究問題的目的和意義以及研究思路。其次,通過廣泛詳細討論的基礎(chǔ)上,設(shè)計了調(diào)查問卷和訪談提綱,對內(nèi)蒙古地區(qū)某幾所高中教師算法教學(xué)及學(xué)生學(xué)習(xí)算法的認識和態(tài)度以及存在的問題進行了調(diào)查研究,對算法教學(xué)研究找到現(xiàn)實依據(jù)。第三,依據(jù)文獻研究和調(diào)查訪談研究結(jié)果分析,結(jié)合學(xué)科內(nèi)容和學(xué)情,參照教與學(xué)相關(guān)理論,研究設(shè)計了具體的算法教學(xué)案例,并提出一些算法教學(xué)的實施建議。
[Abstract]:In 20th century, great changes have taken place in mathematics science and education, which have two important signs: one is the change in the field of mathematics application; The other is the synchronous development of mathematics and computer application technology. The father of computers, von Neumann and Turing, are both famous mathematicians. One aspect, whether the development of computer hardware or the upgrading of computer software, is inseparable from the design of algorithms. On the other hand, the rapid development of computer technology has also played a great role in promoting the development of mathematics, expanding the field of mathematical research, and greatly enriching the methods and methods of mathematical research. It strengthens the relationship between mathematics and other disciplines and widens the fields of application of mathematics. Programming, namely, algorithm design, has permeated many branches of mathematics. "algorithm" is a very good carrier to cultivate the ability of logical reasoning. The idea of algorithm is a main line of elementary mathematics learning. The so-called algorithm refers to the procedural or mechanized thinking process of solving a problem step by step according to some steps, while the so-called logic refers to the fact that the individual is based on objective reality. The thinking process of judging the conclusion of the problem according to a certain recursive relation. The clear procedure thought of solving the problem step by step is the practical need of every individual's development. The algorithm is not a very strange knowledge, although, Some people are not familiar with this concept, but the idea of algorithms often appears in a lot of mathematical content, for example, solving equations, equations, inequalities, geometric mapping or proof, solving linear programming problems, and so on. It can be said that it is an algorithm problem. The characteristic of the algorithm is that it can be operated and tested, and some teachers are trying to combine the content of "algorithm" with computer programming organically. This will also play a good role in fostering students' interest in mathematics. For mathematics teachers, it is not difficult, and after training, there are no difficulties. Some regions have taken some effective measures (for example, dividing up groups and dividing classes to prepare classes). Collective discussion, teaching plan sharing can solve this problem very well. The way of solving or proving the problem by "algorithm" is shown in the form of block diagram. The algorithm block diagram of a problem can make the process of solving this problem very clear. Very intuitive, very concise, very accurate. Based on the idea of improving the practical effect of algorithm teaching and improving the ability to use algorithm ideas and methods to solve practical problems, We have done some research from the following aspects: firstly, through literature analysis and classroom observation, we understand the current situation of algorithm teaching research at home and abroad and the current situation and existing problems in high school algorithm teaching. The purpose and significance of the research and the research ideas are clarified. Secondly, based on the extensive and detailed discussion, the questionnaire and interview outline are designed. This paper investigates the cognition, attitude and existing problems of some high school teachers' algorithm teaching and students' learning algorithm in Inner Mongolia, and finds the realistic basis for the algorithm teaching research. Based on the analysis of the results of literature research and interview, combined with the subject content and learning situation, and referring to the relevant theories of teaching and learning, this paper studies and designs specific cases of algorithmic teaching, and puts forward some suggestions for the implementation of algorithmic teaching.
【學(xué)位授予單位】：內(nèi)蒙古師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：G633.6

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